Stopping power of rifle slugs

[mathwonk]

TL;DR Summary

does physics recommend a heavy bullet or fast one?

As a child, one of my family friends was an 80 year old neighbor, Harry R. Caldwell, who had been a famous tiger hunter in his youth. He killed tigers and Kodiak bears with a .22 or .25 caliber high power load that some felt too small for big game.
[edit: the claim about the bear is false. see later posts.]
He was an exceptional shot, and courageous, but I wonder if physics backs up his faith in the high velocity load as opposed to the slower, heavier load that was more common. Or was he just that good?? Is this just E = MV^2?
https://gunsmagazine.com/discover/harry-caldwells-tigers/
https://en.wikipedia.org/wiki/.22_Savage_Hi-Power

 

[erobz]

Without researching it my first thoughts are that it’s complicated. On a basic level I think we are looking at kinetic energy of the bullet at a particular range. So, we have to predict the muzzle velocity, and the drag coefficients (drag force) acting once the projectile leaves the muzzle.

For a fixed load I would think we have mass$m$ and muzzle velocity $v$ competing inversely with each other. So we could pretend that the force propelling a bullet through a distance $L$ is constant $F_l$ for some amount of powder and examine:

$$F_l = m \frac{dv}{dx} v $$

and find that:

$$ v^2(m) = \frac{2 F_l L}{m}$$

That gives a muzzle kinetic energy:

$$ KE =\frac{1}{2}mv^2 = \frac{1}{2} m \frac{2 F_l L}{m} = F_l L $$

i.e Work equals force times distance. The model almost definitely simplifies away too much reality( I suspect you are looking to go deep), and let me just say that before anyone starts saying how complicated it actually is, I just wanted to get the ball rolling and see how this would naturally develop from here.

Next, I would add a quadratic drag force and solve for the KE at some horizontal range assuming vertical velocity to be negligible in these small range $R$ shots:

$$ F_d = -\beta v^2 = m \frac{dv}{dR} v $$

 

[BWV]

Isn’t it simply that kinetic energy increases linearly with mass but by the square of velocity?

 

[Tom.G]

Isn’t it simply that kinetic energy increases linearly with mass but by the square of velocity?

Sure. But...
Maybe a limiting case should be considered; such as shooting big game with a needle instead of a .25 caliber bullet.

Wouldn't the needle have a high probability of going completely thru the target with minimal damage?

Cheers,
Tom

 

[russ_watters]

Do hunters use hollow points? That's how you ensure maximum damage.

 

[BWV]

Sure. But...
Maybe a limiting case should be considered; such as shooting big game with a needle instead of a .25 caliber bullet.

Wouldn't the needle have a high probability of going completely thru the target with minimal damage?

Cheers,
Tom

The limiting case is velocity, not mass. You can’t drive the needle fast enough given the limits of chemical propulsion and air resistance. A relativistic needle, on the other hand …

 

[morrobay]

Well the link says he killed one tiger. And hunting a kodiak bear with a .22 savage?? Is unheard of. The minimum caliber for that bear is a .30-06.Preferably a .338.

 

[erobz]

Do hunters use hollow points? That's how you ensure maximum damage.

Personally no, Ballistic tips. But I agree, for maximum damage deformation on impact is crucial.

 

[Frabjous]

There is a maximum velocity. Once the bullet exits the body with “sufficient” velocity, energy is being wasted.

 

[Vanadium 50]

I predict that unless "stopping power" is better defined (at best we are using the Potter Stewart "I know it when I see it") this thread will go in circles.

Momentum matters. Energy transferred matters. If you don't somehow quantify the relative degree of these, you cannot calculate an answer.

 

[erobz]

Next, I would add a quadratic drag force and solve for the KE at some horizontal range assuming vertical velocity to be negligible in these small range $R$ shots:

$$ F_d = -\beta v^2 = m \frac{dv}{dR} v $$

Picking up with this get for the kinetic energy of the bullet ( mass $m$) at some range $R$:

$$ KE(R,m)= F_l L e^{ \frac{-2 \beta }{m}R}$$

Seems like a reasonable place to start before taking about what happens upon impact?

 

[Dullard]

In my experience, the 'high velocity needle' case is under-appreciated. Some wounds from an M-16 are small. Wounds where that very energetic round (with high rotation) deforms (striking bone...) and tumbles are... very effective.

 

[mathwonk]

Concerning the remark that he only killed one tiger with a .22, as I recall Harry telling me the story, his usual choice was a .25 caliber bullet, but once he encountered a tiger in the road right in front of him when he was holding his .22. So when it leaped at him he had no choice but to shoot it with that gun, without even time to aim. He said it fell dead only a few feet from his leading foot. Over the years he killed many tigers, perhaps mostly with the .25.

He made the (then) world record big horn sheep (Ovis comosa) kill in 1919, also with a Savage rifle, but I do not know the caliber. The sheep were shot from hundreds of yards away (he mentions 500 yards as maximal practical range in his book, Blue Tiger). Since he spoke of killing the tiger with a .22 only out of necessity, no doubt he picked a larger load for the Kodiak bear. I no longer have the typescript of his unpublished book describing that Alaska trip in detail. All I remember him emphasizing was his confidence, against advice, in the high velocity load, which confidence he said was borne out, even with the bear. But perhaps crucial is the fact he was an extremely good shot.

I once saw his rifle, or a repair/replacement which had been done for free (due to what we see is "your history with our company") by the Savage arms company when his own had been damaged in transit. He said they apologized that they could not reproduce it exactly, since the craftsmen who did it had retired, and I recall the metal on his gun was engraved with tigers on one side and big horn sheep on the other, and the work looked fine to me.

 

[Janus]

Concerning the remark that he only killed one tiger with a .22, as Harry told me the story, his usual choice was a .25 caliber bullet, but once he encountered a tiger in the road right in front of him when he was holding his .22. So when it leaped at him he had no choice but to shoot it with that gun. As he said, it fell dead only a few feet from his leading foot. Over the years he killed many tigers, probably mostly with the .25. He made the (then) world record big horn sheep (Ovis comosa) kill in 1919, also with a Savage rifle, but I do not know the caliber. The sheep were shot from hundreds of yards away. Since he mentions killing the tiger with a .22 only out of necessity, no doubt he picked a larger load for the Kodiak bear, perhaps the .25. All I remember him emphasizing was his confidence, against advice, in the high velocity load, which confidence he said was borne out, even with the bear.

The distance to the target plays a role here. A larger slug has more mass per surface area than a smaller one, so is going to lose velocity over distance less and be more effective at long range. It sounds like this was a close range shot, so under these circumstances, this becomes less of a factor.

 

[berkeman]

I predict that unless "stopping power" is better defined (at best we are using the Potter Stewart "I know it when I see it") this thread will go in circles.

Yes, clearly.

From my EMS training (and some hunting experience), stopping power is generally measured by the wound channel size and characteristics. Ballistic gel blocks are used in experimental work to compare different calibers and loads and bullet characteristics.

I did a Google search on wound channel ballistics and got lots of good hits. Here is one from that hit list:

https://whitemountainforensic.com/wound-ballistics-motion-effects-projectiles-human-body/

Unfortunately @Dr. Courtney has not been at PF for the last couple of years -- wound ballistics is one of his main areas of research, IIRC. He could probably add a lot to this thread.

 

[mathwonk]

As to Reverend Caldwell's weapon of choice, at least at one point in time, here are words from his own book, The Blue Tiger, pub. 1925, p.5 (fifth page of text, p.17 in first edition, 1924), when he was being interviewed by village elders in China about helping them dispose of a man - eating tiger, having already killed one in the vicinity some months earlier:
"As soon as I had settled in the elder's home, I pulled out my tiger gun and began to try its action. The gun itself interested the people much, but the little sharp- pointed cartridges even more. I was using a twenty-two calibre high-power Savage rifle at the time, and people could not conceive that such a light-weight gun and such a small ball would be effective with an animal such as I was after. Excitement ran very high."
https://babel.hathitrust.org/cgi/pt?id=uc1.$b271486&seq=9

In regard to this whole question of killing power, it may also matter whether the bullet hits the target in the heart or between the eyes, which my friend may have been more capable of than average, as opposed to some random body shot.

As an extreme example, when charged by a Kodiak bear, one hunter he was guiding actually threw down his own weapon without firing and began to run, and the Rev. Caldwell had to kill the bear to save him.

 

[mathwonk]

Update: Indeed, as predicted here by morrobay, neither the .22 nor .25 was considered suitable for Kodiak bear.
According to his granddaughter, in his unpublished autobiography, "Papa" Caldwell asked Savage arms for "a rifle appropriate for bears. They sent him a .300 caliber rifle, with which Papa killed at least one bear with '150 grain balls.' Another hunter had to use three 250 grain balls to bring down a huge bear."

Now I think I get it. We tell stories, and remember them, that feature our most unusual and spectacular accomplishments, not the ones that are everyday fare. So it seems that what I recalled as my friend's standard behavior was more like something he pulled off at least once. Still it seems he was a remarkable hunter.

 

[erobz]

Update: Indeed, as predicted here by morrobay, neither the .22 nor .25 was considered suitable for Kodiak bear.
According to his granddaughter, in his unpublished autobiography, "Papa" Caldwell asked Savage arms for "a rifle appropriate for bears. They sent him a .300 caliber rifle, with which Papa killed at least one bear with '150 grain balls.' Another hunter had to use three 250 grain balls to bring down a huge bear."

Now I think I get it. We tell stories, and remember them, that feature our most unusual and spectacular accomplishments, not the ones that are everyday fare. So it seems that what I recalled as my friend's standard behavior was more like something he pulled off at least once. Still it seems he was a remarkable hunter.

Can you shoot a grizzly in the juggler with a .22 caliber and kill it...probably. The question is will it rip your face off before it succumbs! I always hunt with more than what is needed in that sense. Thats usually important if you wish to minimize risk of suffering in the hunt. I also know people get bears with compound bows...so there is that too.

 

[berkeman]

I also know people get bears with compound bows...so there is that too.

Not me. When I hunted deer with a bow, I always carried my .357 magnum pistol, which is not allowed in Cali (no firearms are allowed in possession while bow hunting). I was not comfortable being way out in the woods without a firearm when bowhunting, so I figured I'd just plead my case to the judge if I ever got cited.

Nope, not going to happen...

https://www.eastidahonews.com/2024/09/adult-male-grizzly-bear-attacks-archery-hunter-in-island-park/

 

[erobz]

so I figured I'd just plead my case to the judge if I ever got cited.

Better to plead your case with the game commission than the grizzly!

 

[berkeman]

Better to plead your case with the game commission than the grizzly!

I've only run away from two things in the woods, even though I'm usually armed. First was a skunk that I stumbled across in the dark while I was sneaking into my deer hunting spot. The second was a cute baby bear that I encountered and I couldn't tell where the mama bear was.

 

[mathwonk]

My wife said she read that when encountering a bear, one should calmly back away. Once in the Olympics with our son, while focusing on a flower with her camera she heard him say "mom, come here". After she ignored him once or twice, she asked "why", and his response was "mother bear, two cubs". Totally forgetting her reading, she ran shouting roughly "sh****t" through the nearby woods. All turned out well, but there was a somewhat sleepless night.

 

[erobz]

If its black, don't crack. If it's brown, lie down. If it's white...good night.

 

[Mondayman]

A Cree trapper named Bella Twin shot and killed a large grizzly with a Cooey Ace single shot .22 rifle up near Slave Lake. Her first shot got it in the eye, and then she put seven more rounds into its head. The rifle is at the Royal Alberta Museum in Edmonton. The bear skull is still with the family. So it has been done before. I don't know if the bear was charging or not. Either way, it's quite a lucky shot. One I wouldn't count on making again.

When it comes to bear defense, I want something heavy. Like .338 WM or a .45-70 guide gun. A bear can run for a long time while bleeding out - unless you hit it's heart or penetrate the skull and hit it in the brain, you're in trouble. When we go deep into backcountry I bring my Remington with slugs. Atleast with a slug or a 405g Buffalo Bore .45-70, you can do signifcant damage to a bear even if you hit it in the shoulder. But we've never had any issues with bears here luckily. If you travel in groups and make noise you're unlikely to run into trouble. Closest call I ever had was when a black bear came out of nowhere and walked past me while I was taking a poop, maybe ten yards away. Didn't even look at me.

 

[mathwonk]

Thanks for the story of Bella Twin. Here is a detailed account that suggests the shot, although certainly fortunate, was carefully targeted.
https://www.ammoland.com/2017/06/be...-take-the-1953-world-record-grizzly-and-more/

Here is another detailed, slightly different, account:
http://www.bear-hunting.com/tactics?ID=6FD66CD5-9198-440F-B517-A71C6D1F8748

 

[jbriggs444]

My closest call with a bear was as a teen, canoe camping with my parents on the shore of lake Bitchu in Quetico. Our usual island campsite nearby in lake Bemar was taken, so we risked camping on the mainland. A bear prowled through the site that night and ran off with one of our Duluth packs in its jaws. A non-food pack. We had hoisted the food pack aloft out of reach. My dad chased after. Disconcerted, the bear dropped the pack and scampered off. The main result was a large tooth mark on the binocular case inside the pack.

 

[JT Smith]

Black bears are rarely a problem other than to food or property. It was just this year that the very first recorded death due to a black bear in California occurred. Deer Dear are more dangerous.

 

[mathwonk]

what is wrong with/scary about this? "My dad chased after. "

we live in a rural area and have bear, coyote and deer in our yard regularly, but we don't shoot or chase after them. they just like our blackberries and garden vegetables. I do clean my outdoor grill regularly, and close the windows at night.

 

[berkeman]

what is wrong with/scary about this? "My dad chased after. "

LOL, he was only a Darwin Award runner-up (I see what I did there).

 

[sophiecentaur]

Didn't even look at me.

He must have been well up-wind of you, with the sun in his eyes.

 

[cjl]

There is a maximum velocity. Once the bullet exits the body with “sufficient” velocity, energy is being wasted.

Yes and no?

Higher velocity doesn't actually necessarily mean more penetration. Extremely high velocity can cause massive hydrostatic shock on impact, causing pressures that can break up the bullet or cause it to tumble and that can also cause it to dump energy much faster than a lower velocity round would. In some cases, a very high velocity small round can have *less* penetration than a large slow round with the same energy, while causing much more damage near the initial entry wound. For an example of this, look how fast a .22-250 dumps its energy in this test:



That having been said, even the highest velocity 22 caliber rounds (220 swift) would make me nervous with something like a grizzly or moose. In theory, it should have plenty of energy, but I'd still feel more comfortable with something a bit more powerful.